Video poker has become very popular. One of the most common variations of video poker is Five Card Draw Poker. In general, for a play of a Five Card Draw Poker game, a gaming system deals a player a hand of five cards face up from a fifty-two card deck of playing cards. The gaming system enables the player to discard none of, one of, a plurality of but less than all of, or all of the five cards from the player's hand. The gaming system replaces each discarded card with another card from the deck. After replacing any discarded cards, the gaming system evaluates the cards of the player's hand against a paytable to determine whether the player's hand forms a winning hand associated with one of a plurality of different winning hand categories.